Block #460,689

TWNLength 10★★☆☆☆

Bi-Twin Chain · Discovered 3/26/2014, 5:12:54 AM · Difficulty 10.4144 · 6,345,369 confirmations

TWN

Bi-Twin Chain

Interleaved pairs of primes that differ by 2, forming twin prime pairs at each level.

Block Header

Block Hash

db725acc161cd1cca80e7a97da8bd6738dfee7825183530f24e29266cfc45674

View on Chainz ↗

Height

#460,689

Difficulty

10.414410

Transactions

Size

1.09 KB

Version

Bits

0a6a16cb

Nonce

206,392

Timestamp

3/26/2014, 5:12:54 AM

Confirmations

6,345,369

Mined by

⛏️ P2SHAeKNrjNjtSncLJjUrDnQbrfzMS1NEq95Ta

Merkle Root

c07ef79ffb695f6f8452868ff96fcfdeb3b4ac4c092f02f6e9280b433712246a

Transactions (3)

Coinbaseacb7a7b152180f…ab85d9ac8d7d99

1 in → 1 out9.2300 XPM110 B

AeKNrjNj…1NEq95Ta

3f02130cafe303…56e30ba2073df0

2 in → 7 out13.4666 XPM544 B

AR4Wc6UY…Nq4ijpFb AZKgQwBY…rTXiwBnJ AR8B7Nhz…wBcyL3zC AUAjjeWc…gzysQzwJ AR6A5Nju…cdLFG7Cw

4d67634801c980…d3538b773cc595

2 in → 2 out49.1950 XPM372 B

Aa1AvAie…Yv4xhXZC AG5dtdfk…a8dH8EqH

Prime Chain Origin

This is the prime chain origin stored in the block header. It is a composite number (not prime itself) — it equals the first prime in the chain multiplied by a primorial. The origin anchors the entire chain to this specific block.

5.987 × 10⁹⁶(97-digit number)

59877151032147580935…85847598646517118079

Discovered Prime Numbers

Lower: 2^k × origin − 1 | Upper: 2^k × origin + 1

These are the actual prime numbers discovered by this block, computed using the verified Primecoin formula. Each number has been independently confirmed to pass the Fermat primality test. Use the FactorDB links to verify any number independently.

Level 0 — Twin Prime Pair (origin ± 1)

origin − 1

5.987 × 10⁹⁶(97-digit number)

59877151032147580935…85847598646517118079

Verify on FactorDB ↗Wolfram Alpha ↗

origin + 1

5.987 × 10⁹⁶(97-digit number)

59877151032147580935…85847598646517118081

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: origin + 1 − origin − 1 = 2 (twin primes ✓)

Level 1 — Twin Prime Pair (2^1 × origin ± 1)

2^1 × origin − 1

1.197 × 10⁹⁷(98-digit number)

11975430206429516187…71695197293034236159

Verify on FactorDB ↗Wolfram Alpha ↗

2^1 × origin + 1

1.197 × 10⁹⁷(98-digit number)

11975430206429516187…71695197293034236161

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^1 × origin + 1 − 2^1 × origin − 1 = 2 (twin primes ✓)

Level 2 — Twin Prime Pair (2^2 × origin ± 1)

2^2 × origin − 1

2.395 × 10⁹⁷(98-digit number)

23950860412859032374…43390394586068472319

Verify on FactorDB ↗Wolfram Alpha ↗

2^2 × origin + 1

2.395 × 10⁹⁷(98-digit number)

23950860412859032374…43390394586068472321

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^2 × origin + 1 − 2^2 × origin − 1 = 2 (twin primes ✓)

Level 3 — Twin Prime Pair (2^3 × origin ± 1)

2^3 × origin − 1

4.790 × 10⁹⁷(98-digit number)

47901720825718064748…86780789172136944639

Verify on FactorDB ↗Wolfram Alpha ↗

2^3 × origin + 1

4.790 × 10⁹⁷(98-digit number)

47901720825718064748…86780789172136944641

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^3 × origin + 1 − 2^3 × origin − 1 = 2 (twin primes ✓)

Level 4 — Twin Prime Pair (2^4 × origin ± 1)

2^4 × origin − 1

9.580 × 10⁹⁷(98-digit number)

95803441651436129497…73561578344273889279

Verify on FactorDB ↗Wolfram Alpha ↗

2^4 × origin + 1

9.580 × 10⁹⁷(98-digit number)

95803441651436129497…73561578344273889281

Verify on FactorDB ↗Wolfram Alpha ↗

Difference: 2^4 × origin + 1 − 2^4 × origin − 1 = 2 (twin primes ✓)

What this block proved

The miner who found this block proved the existence of 10 consecutive prime numbers forming a Bi-Twin Chain. The prime chain origin — the large number shown above — anchors the chain and is divisible by a primorial (the product of small primes), cryptographically tying these prime numbers to this specific block.

★★☆☆☆

Rarity

UncommonChain length 10

Roughly 1 in 100 blocks. Solid but expected in a healthy network.

How Primecoin's Proof-of-Work Constructs These Primes

Primecoin stores a value called the prime chain origin in each block. The miner found a large integer such that when divided by a primorial (the product of small primes: 2 × 3 × 5 × 7 × …), the result is the first prime in the chain. The origin is deliberately divisible by this primorial — that divisibility is part of the proof.

Prime Chain Origin = First Prime × Primorial (2·3·5·7·11·…)

Source: Primecoin prime.cpp — CheckPrimeProofOfWork()

This is why the origin has many small prime factors — those factors are the primorial divisor. The chain then extends from the first prime using the TWN formula:

TWN: twin pairs (p, p+2) where p = origin/primorial − 1 and p+2 = origin/primorial + 1

Cross-reference on Chainz Explorer